On a generalized canonical bundle formula for generically finite morphisms
Jingjun Han, Wenfei Liu
Abstract
We prove a canonical bundle formula for generically finite morphisms in the setting of generalized pairs (with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ℝ</mml:mi> </mml:math> -coefficients). This complements Filipazzi’s canonical bundle formula for morphisms with connected fibres. It is then applied to obtain a subadjunction formula for log canonical centers of generalized pairs. As another application, we show that the image of an anti-nef log canonical generalized pair has the structure of a numerically trivial log canonical generalized pair. This readily implies a result of Chen–Zhang. Along the way we prove that the Shokurov type convex sets for anti-nef log canonical divisors are indeed rational polyhedral sets.